Is there a way to derive IEqualityComparer from IComparer?

It's not possible to implement an IComparer from an IEqualityComparer as you have no way of knowing whether an unequal item is greater than or less than the other item.

It's not possible to implement an IEqualityComparer from an IComparer as there's no way for you to generate a hash code that is in line with the IComparer's identity.

That said, there's no need for you to have both types of comparers in your case. When computing LRU you're comparing the time since an item was used as the primary comparer and then comparing based on a passed in comparer as a tiebreaker. Just remove that last part; don't have a tiebreaker. Let it be undefined which item leaves the cache when there is a tie for the least recently used. When you do that you only need to accept an IEqualityComparer, not an IComparer.

As I alluded to in my comment, you could add a helper method that might make things a little simpler for a basic use case:

public class LFUCache<TKey,TValue>
{
    public static LFUCache<TKey, TValue> Create<TComp>(int capacity, TComp comparer) where TComp : IEqualityComparer<TKey>, IComparer<TKey>
    {
        return new LFUCache<TKey, TValue>(capacity, comparer, comparer);
    }
}

and you'd use it like this:

var cache = LFUCache<string, int>.Create(10000, StringComparer.InvariantCultureIgnoreCase);